10.2 Multiplying Polynomials \( \begin{array}{l}\text { 1) } x\left(2 x^{2}-3 x+9\right) \\ 2 x^{3}-3 x^{2}+9 x\end{array} \)

Did you know that the distributive property is key when multiplying polynomials? It’s like handing out slices of pizza to your friends; you need to make sure everyone gets their fair share! When multiplying \(x\) by each term in the polynomial \(2x^2 - 3x + 9\), distribute \(x\) across all three terms, which gives you \(2x^3 - 3x^2 + 9x\). Easy peasy, right? One common mistake is forgetting to apply the exponent rules while multiplying. Remember, when you multiply like bases, you add the exponents! But in this case, you only have the variable \(x\) multiplied by the polynomial, so you just bring over the power of \(x\) as you distribute. Watch out for those pesky sign changes too!